New method for invariant neural networks using probabilistic symmetries.
problem Improving neural network performance in data-scarce, non-i.i.d., or unsupervised settings.
method Characterizing neural network structures invariant under compact group actions using probabilistic symmetry.
result Established a link between functional and probabilistic symmetry, yielding generative representations of invariant distributions.
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over the model's parameters, which can pose challenges both for performing inference a…
Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.
problem Improving simultaneous inference in complex settings like arrays and graphs.
method Generalized empirical Bayes approach based on probabilistic symmetry.
result BEB outperforms existing methods in denoising arrays and spatial data.
Improves convergence speed in compressive sensing with a new probabilistic approach.
problem Efficiently solving the best subset selection problem in compressive sensing.
method Smooth probabilistic reformulation of ℓ0 regularized regression. result Empirically outperforms existing compressive sensing algorithms across various settings.
Efficiently infers cluster assignments in probabilistic models.
problem Efficiently inferring cluster assignments in probabilistic models.
method Amortized approximate Bayesian inference mapping cluster representations into conditional probabilities.
result Parallelizable, yields iid samples with similar computational cost to Gibbs sampling.
We solve Bayesian PCA's rotational symmetry issue by rotation-invariant parameterization.
problem Bayesian PCA's rotational symmetry complicates inference and interpretation.
method Rotation-invariant Householder parameterization using random matrix theory.
result Efficient rotation-invariant probabilistic PCA implementation.
The paper defines symmetries in no-arbitrage markets.
problem Characterizing transformations preserving no-arbitrage.
method Geometric formalization in discrete time models.
result Local characterization of no-arbitrage symmetries.
SymPE breaks symmetries in equivariant networks, improving performance across various tasks.
problem Equivariant networks cannot break symmetries, leading to poor performance in tasks with symmetrical inputs.
method Novel equivariant conditional distributions and randomized canonicalization.
result SymPE significantly improves performance of group-equivariant and graph neural networks.
Bayesian framework detects symmetries in chaotic dynamical systems.
problem Detecting symmetries in chaotic attractors for insights into dynamical system structure.
method Bayesian framework using Gibbs posterior constructed from Wasserstein distances.
result Bayesian framework accurately recovers symmetries under high noise and small sample sizes.
Efficiently samples and learns densities with symmetries using equivariant methods.
problem Efficiently sampling and learning densities with symmetries.
method Equivariant Stein Variational Gradient Descent (SVGD) and equivariant energy based models.
result Improves and scales up training of energy based models.
Extends DeTEcT framework for token economies with dynamic and probabilistic parameters.
problem Modeling wealth distribution in token economies with dynamic and probabilistic parameters.
method Introduces four parametrization techniques: dynamic vs static, probabilistic vs non-probabilistic.
result Derives existing wealth distribution models from DeTEcT framework with added restrictions.
Two approximate lifted variational methods for hybrid domains improve inference scalability and accuracy.
problem Efficient inference in hybrid probabilistic relational models with multi-modality and continuous evidence.
method Two approximate lifted variational approaches applicable to hybrid domains, exploiting model symmetries.
result The proposed variational methods are scalable and can leverage approximate model symmetries, outperforming existing message-passing approaches.
Learn class-invariant and symmetry-equivariant representations for multi-class data.
problem Deep neural networks learn opaque representations; we aim to make them more transparent.
method Probabilistic modelling with two separate latent variables: invariant and equivariant.
result Qualitative and quantitative performance competitive with other methods, with little tuning.
Paper develops a differentiable approach for 3D imaging models using Fourier slice theorem.
problem Uncertainty in 3D structure modeling and pose estimation in scientific imaging.
method Differentiable probabilistic models in Fourier space with backpropagation through projection.
result Validates approach on 3D protein reconstruction and extends to probabilistic models.
New approach resolves ambiguity in PPCA model's maximum likelihood estimation.
problem Ambiguity in maximum likelihood estimation of PPCA model due to rotational symmetry.
method Using quotient topological spaces, the approach resolves ambiguity and shows consistency of the maximum likelihood solution.
result Maximum likelihood solution is consistent in an appropriate quotient Euclidean space.
Extends probabilistic approach for Kahler-Einstein metrics on Fano manifolds.
problem Constructing Kahler-Einstein metrics on log Fano manifolds with non-discrete automorphism groups.
method Introduces Gibbs polystability and uses moment map constraint to break symmetry.
result Gibbs polystability conjectured to be equivalent to existence of Kahler-Einstein metric.
Trained MLPs' weights are exchangeable, leading to stable kernel behavior.
problem Assumptions of IID parameters in trained models are violated.
method Showed weights in MLPs are exchangeable and identified kernel stability.
result Layer-wise kernel of fully-connected layers remains approximately constant during training.
We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of availa…
A new algorithm converts staged trees into Chain Event Graphs.
problem Creating explicit representations of structural zeros and conditional independences.
method Iterative backward algorithm transforming a staged tree into a CEG.
result No information is lost in the transformation from staged tree to CEG.
The paper analyzes symmetries of Vaidya-Bonner geodesics.
problem Investigating invariance properties of Vaidya-Bonner geodesics.
method Classification of Lie point symmetries and Noether symmetries, determination of optimal system of subalgebras.
result Determination of optimal system of subalgebras for Vaidya-Bonner geodesics.
New method detects symmetries beyond affine transformations.
problem Current methods limit symmetry detection to affine transformations.
method Framework for discovering continuous symmetry beyond affine transformations.
result Method is competitive for large sample sizes and superior for small sample sizes.
Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism with a computational model remains elusive. Motivated by a new study demonstrating the extremely high inter-person accuracy of human perceived symmetries in the wild, we have constructed the first …
Classifies symmetries of non-flat 3-webs around a point.
problem Understanding symmetries of non-flat 3-webs.
method Classification and construction methods for symmetries.
result Classification of symmetries for non-flat 3-webs.
Geometric mechanism mimics physics' symmetry breaking.
problem Understanding spontaneous symmetry breaking in geometry.
method Analogous to physics, studying symmetry breaking in differential geometry.
result Symmetry breaking can be used to solve geometric problems.
Method improves deep learning models for datasets with mixed approximate symmetries.
problem Improving deep learning models for datasets with mixed approximate symmetries.
method Regularizer-based approach to build models for datasets with mixed approximate symmetries.
result Our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.
Researchers construct a probabilistic model for a WZW theory on hyperbolic space and link it to Liouville theory.
problem Rigorous probabilistic construction of WZW models on curved spaces.
method Path integral approach on closed Riemann surfaces twisted by gauge fields.
result Correspondence between correlation functions of H3-WZW and Liouville CFT. PENs learn summary statistics for ABC using invariant neural architectures.
problem Learning summary statistics for approximate Bayesian computation (ABC).
method Partially exchangeable networks (PENs) that are invariant to block-switch transformations.
result PENs provide more reliable posterior samples with less training data.
Symmetry in loss functions constrains model parameters, leading to specific learning outcomes.
problem Understanding and leveraging symmetries in neural networks to improve learning outcomes.
method Analyzing the impact of loss function symmetries on model parameters and learning behavior.
result Mirror-reflection symmetries in loss functions lead to constraints on model parameters, influencing learning outcomes.
Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of the geodesic equations, two different approaches to study the approximate symmet…
New symmetry dimensions for higher order ODEs are identified.
problem Determining the maximal and submaximal symmetry dimensions for higher order ODEs.
method Cartan-geometric approach to classify symmetry dimensions.
result Next largest realizable symmetry dimensions for scalar ODEs of order ≥ 4 and vector ODEs of order ≥ 3 are determined.
Generalizes symmetries of curved manifolds.
problem Maximizing symmetries in curved manifolds.
method Replaces torus with abelian group, generalizes results.
result Generalizes symmetry results for positively curved manifolds.
New framework discovers non-affine continuous symmetries in neural networks.
problem Lack of efficient methods for detecting non-affine continuous symmetries in neural networks.
method Computational framework for discovering infinitesimal generators of multi-parameter group actions.
result Framework can discover non-affine continuous symmetries in neural networks.
Study of continuous symmetries in Nahm data and BPS monopoles.
problem Solutions to Nahm's equations with continuous symmetries.
method Classification of Ansätze and construction of Nahm data.
result Construction of new BPS monopoles with spherical symmetry.
Symmetry in neural networks reduces parameter count without sacrificing accuracy.
problem Improving parameter usage and efficiency in deep neural networks.
method Imposing symmetry constraints on neural network parameters, especially in convolutional and recurrent networks.
result Symmetry can have little or no negative effect on network accuracy, even in deep overparameterized networks.
Researchers discover symmetries in Ricci flows and use them to find invariant solutions.
problem Finding symmetries in Ricci flows on manifolds.
method Developed a method to find Lie point symmetries of Ricci flows and particular metrics.
result Invariant solutions of Ricci flow for specific metric families were obtained.
Algorithm designs neural group actions for symmetric transformations.
problem Designing neural networks for symmetric transformations.
method Develops Neural Group Actions (NGAs) for finite groups, enforcing volume-preserving constraints.
result Demonstrates NGAs for the quaternion group Q8 can learn quantum gate transformations. This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have symmetries with hidden extensions, then we further extend these to hidden symmetries of…
New symmetry found in colored Alexander polynomial.
problem Understanding the structure of colored Alexander polynomials.
method Study of loop and character expansions, group theoretic constraints.
result Existence of a new symmetry in the colored HOMFLY-PT polynomial.
Symmetry in finance is a neglected but potentially valuable concept.
problem The underutilization of symmetry in financial markets.
method Examining symmetry in game theory, technical analysis, and long-term economic growth.
result Symmetry principles can be applied to financial strategies and market dynamics.
Symmetry of neural network densities can be determined from correlation functions.
problem Determining symmetries of neural network densities without knowing the density itself.
method Symmetry-via-duality approach using invariance properties of correlation functions.
result Symmetries of neural network densities can be determined via dual computations of correlation functions.
Clarifies relation between Pfaffian fibrations and relative algebroids.
problem Understanding geometric structures and symmetries in PDEs.
method Introduces and analyzes Pfaffian fibrations and relative algebroids, clarifying their relationship.
result Every Pfaffian fibration induces a relative algebroid, and their prolongations and local solutions coincide.
Symmetries in shrinking Ricci solitons spread outward.
problem Understanding symmetries in shrinking Ricci solitons.
method Propagating approximate symmetries to larger scales.
result Symmetries in shrinking Ricci solitons spread outward.
Classifies Lie symmetry algebras for 2D quasilinear equations, linking symmetry to linearity.
problem Classifying Lie symmetry algebras for 2D quasilinear equations.
method Classification based on abelian Lie symmetry algebras of dimension and rank.
result Equations with specific symmetry algebras are linearizable.
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
problem Improving graph neural network performance on asymmetric graphs.
method Formalizing approximate symmetries via graph coarsening, introducing a bias-variance formula.
result Best generalization performance achieved by choosing a larger symmetry group than automorphisms but smaller than permutations.
Noether's theorem clarifies how symmetries in neural networks influence learning.
problem Understanding how symmetries in neural networks affect learning.
method Systematic study of symmetry interactions with learning algorithms using Noether's theorem.
result Symmetries impose restrictions on the optimization path, leading to conserved quantities.
This paper aims to incorporate passive symmetries in machine learning for better generalization.
problem Machine learning's reliance on arbitrary choices leads to passive symmetries that can limit generalization.
method Translation among physics, mathematics, and machine learning to understand and implement passive symmetries.
result Respecting passive symmetries can improve machine learning's ability to generalize.
Researchers create BPS monopoles with any desired symmetry breaking.
problem Creating monopoles with specific symmetry breaking patterns.
method Using a new class of Nahm data to construct finite energy BPS monopoles.
result Arbitrary symmetry breaking monopoles can be constructed.
Study of symmetries in 2D Yang-Mills theory, including orbifolds and higher forms.
problem Understanding symmetries and anomalies in 2D Yang-Mills theory.
method Combining continuum methods, topological defects, and higher gauge theory.
result Unified description of higher and lower form gauge fields, identifying spontaneous symmetry breaking.